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arXiv 2204.07518cs.ITmath.IT
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分布式压缩中的局部解码

Local Decoding in Distributed Compression

Shashank Vatedka, Venkat Chandar, Aslan Tchamkerten

摘要:

最近表明,无损压缩的一个单一的源$X^n$是可实现的强局部性的概念,任何$X_i$可以从一个恒定数量的压缩位解码,在$n$的错误概率为零。相比之下,我们表明,对于两个单独编码的源$(X^n,Y^n)$,无损压缩和强局部性一般是不可能的。具体而言,我们表明,对于类的“混淆”的来源,强本地性不能实现时,其中一个源被压缩到其熵以下。与$n$无关,对于某个索引$i$,解码$(X_i,Y_i)$的错误概率由$2^{-O(d)}$下界,其中$d$表示由本地解码器访问的压缩比特的数量。相反,如果源是不可混淆的,即使其中一个源被压缩到低于其熵,强局域性也是可能的。结果扩展到任意数量的源。

英文摘要:

It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error. By contrast, we show that for two separately encoded sources $(X^n,Y^n)$, lossless compression and strong locality is generally not possible. Specifically, we show that for the class of ``confusable'' sources, strong locality cannot be achieved whenever one of the sources is compressed below its entropy. Irrespective of $n$, for some index $i$ the probability of error of decoding $(X_i,Y_i)$ is lower bounded by $2^{-O(d)}$, where $d$ denotes the number of compressed bits accessed by the local decoder. Conversely, if the source is not confusable, strong locality is possible even if one of the sources is compressed below its entropy. Results extend to an arbitrary number of sources.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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